Particle moving in a one-dimensional potential

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Homework Statement



A particle moving in a one-dimensional potential is in a state such that its wavefunction at time t=0 is:

Psi(x,0)=A(x-a)x, 0<=x<=a, and
Psi(x,0)=0, otherwise.

Sketch |Psi(x,0)|^2, which gives the probability distribution describing the position of the particle at time t=0.

Homework Equations



As above

The Attempt at a Solution



I am thrown by Psi in this question. It doesn't even resemble a wavefunction. Am I simply supposed to square the absolute value of the polynomial?
 

Answers and Replies

  • #2
vela
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Yes. Why do you say it "doesn't even resemble a wavefunction"?
 
  • #3
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Because its not a periodic function.
 
  • #4
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I'm obviously overlooking something important here. Please help.
 
  • #5
HallsofIvy
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Why should it be periodic? Are sure what is meant by a "waveform" here?
 
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Shouldn't a wavefunction resemble a wave? ie be periodic?
 
  • #7
You are confusing a wavefunction with a periodic function such as a sinusoid of varying harmoics, etc. The wavefunction is essentially a probability amplitude for (in this case) the location of a particle.

It is, (in this case) a one dimensional wave and you can model its motion using a (rather famous) relation that looks quite close to the wave equation, shown here:

[ tex ] \nabla^2 f(x,y,z) = \frac{1}{c^2} \frac{\partial f(x,y,z)}{\partial t} [ /tex ]
 
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  • #8
vela
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Shouldn't a wavefunction resemble a wave? ie be periodic?
Nope. A pulse traveling down a string, for instance, is a wave. There's no requirement for periodicity at all.
 
  • #9
by the way....why isn't my tex being formatted?
 

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